Question: Rewrite as a simplified fraction. ${1.12\overline{6} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1126.6666...\\ 100x &= 112.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1014}$ ${x = \dfrac{1014}{900}} $ ${x = \dfrac{169}{150}} \text{or} {1 \dfrac{19}{150}}$